Summary
The insights gained by the concept of deterministic chaos for the EEG is that this seemingly disordered process may be governed by relatively few simple laws which could be determined. One of the quantitative measures of a complex dynamical system is that of its dimension. The term ‘dimension’ refers to the ability of a space to contain a set of points. We estimated the correlational dimension of the EEG and compared the outcome to traditional Fourier analyses. In addition, we tested the hypothesis that the EEG can be described as filtered noise. Data from 15 electrode sites and 31 subjects are reported in the present study. We have utilized a variety of tasks that cut across sensory modalities including touch, vision, and imagery which reflect neuropsychological processes that differentially engage areas of the cortex in the first part of the study. In the second part, the differences between the perception of an object and the imagination of the same object were evaluated. The outcome shows variations between scalp sites for all measures and also variations between tasks in terms of dimensionality of the EEG. The hypothesis of a higher dimensionality ("complexity") of imagery compared to actual perceptual processing was confirmed. A statistical comparison between the maps generated by means of the various measures shows that different informations are extracted when using the different measures. There is also statistical evidence that the EEG cannot completely be described by the model of filtered noise.
Similar content being viewed by others
References
Akima, H. Bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Transactions on Mathematical Software. 1987, 4: 160–164.
Albano, A.M., Abraham, N.B., de Guzman, G.C., Tarroja, M.F.H., Bandy, D.K., Gioggia, R.S., Rapp, P.E., Zimmerman, I.D., Greenbaum, N.N. and Bashore, T.R. Lasers and brains: complex systems with low-dimensional attractors. In: G. Mayer-Kress (Ed.), Dimension and Entropies in Chaotic Systems. Berlin, Heidelberg, New York, Tokyo, Springer, 1986: 231–252.
Babloyantz, A. Strange attractors in the dynamics of brain activity. In: H. Haken (Ed.), Complex Systems - Operational Approaches in Neurobiology, Physics, and Computers. Berlin, Springer, 1985: 116–122.
Babloyantz, A., Salazar, J.M. and Nicolis, C. Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys. Lett., 1985, Vol.111A, 3: 152–156.
Babloyantz, A. and Destexhe, A. Low dimensional chaos in an instance of epilepsy. Proc. Natl. Acad. Sci., 1986, 83: 3513–3517.
Basar, E., Basar-Eroglu, Röschke, J. and Schult, J. Chaos and alpha-preparation in brain function. In: R.M.J. Corterill (Ed.), Models of Brain Function. Cambridge University Press, Cambridge, 1989: 365–395.
Birbaumer, N., Lang, P.J., Cook, E., Elbert, T., Lutzenberger, W. and Rockstroh, B. Slow brain potentials, imagery, and hemispheric differences. Int. J. Neuroscience, 1988, 39: 101–116.
Birbaumer, N., Elbert, T., Canavan, A. and Rockstroh, B. Slow Potentials of the Cerebral Cortex and Behavior. Physiological Reviews, 1990, 70: 1–41.
Birbaumer, N., Lutzenberger, W., Flor, H., Elbert, T. and Rockstroh, B. Imagery and brain processes. In: N. Birbaumer and A. Öhman (Eds), The Organization of Emotions. Hogrefe, Bern, 1992.
Broomhead, D.S. and King, G.P. Extracting qualitative dynamics from experimental data. Physica, 1986, 20D: 217–236.
Desmedt, J.E. and Tomberg, C. Topographic analysis in brain mapping can be compromised by the average reference. Brain Topography, 1990, 3: 35–42.
Farmer, J.D., Ott, E. and York, J.A. Dimension of chaotic attractors, Physica, 1983, 7D: 153–180.
Graf, K.E. and Elbert, T. Dimensional analysis of the waking EEG. In: E. Basar, T.H. Bullock (Eds.), Brain Dynamics. Springer-Verlag, Berlin, Heidelberg, 1989: 174–191.
Lutzenberger, W. and Elbert, T. A/D conversion in DMA-mode- problems and solutions. Psychophysiology, 1991, 28: 607–608.
Mayer-Kress, G. and Holzfuβ, J. Analysis of the human electroencephalogram with methods from nonlinear dynamics. In: L. Rensing, U. an der Heiden, M.C. Mackey (Eds.), Temporal Disorder in Human Oscillatory Systems. Berlin, Heidelberg, New York, Tokyo, Springer, 1987.
Mayer-Kress, G., Yates, F.E., Benton, L., Keidel, M., Tirsch, W., Pöppl, S.J. and Geist, K. Dimensional analysis of nonlinear oscillations in brain, heart, and muscle. Math. Biosciences, 1988, 90: 155–182.
McCall, W.A. Measurement. Wiley, New York, 1939.
McCarthy, P. and Ray, W.J. Interactions between alpha and beta EEG frequencies. Psychophysiology, 1988, 25: 468.
Nan, X. and Jinghua, X. The fractal dimension of EEG as a physical measure of conscious human brain activities. Bulletin of Mathematical Biology, 1988, 50: 559–565.
Phelps, M.E., Mazziotta, S.C., Kuhl, D.E., Nuwer, M., Packwood, J., Metter, J. and Engel, J. Tomographic mapping of human cerebral metabolism: Visual stimulation and deprivation. Neurology, 1981, 31: 517–529.
Pijn, J.P., Van Neerven, J., Noest, A. and Lopes da Silva, F.H. Chaos or noise in EEG signals; dependence on state and brain site. Electroencephalography and Clinical Neurophysiology, 1991, 79: 371–381.
Pritchard, W.S. and Duke, D.W. Deterministic chaos and the human EEG. Psychophysiology, 1990, 27: 56.
Rapp, P.E. Oscillations and chaos in cellular metabolism and physiological systems. In: A.V. Holden, (Ed.), Chaos - Nonlinear Science: Theory and Application. Manchester University Press, 1986: 179–208.
Rapp, P.E., Bashore, T., Martinerie, J., Albano, A., Zimmerman, I., and Mees, A. Dynamics of Brain Electrical Activity. Brain Topography, 1990, 2: 99–118.
Rapp, P.E., Zimmerman, I.D., Albano, A.M., deGuzman, G.C. and Greenbaum, N.N. Dynamics of spontaneous neuronal activity in the simian motor cortex: The dimension of chaotic neurons. Phys. Lett. 110A, 1985, 6: 335.
Rapp, P.E., Zimmerman, I.D., Albano, A.M., deGuzman, G.C., Greenbaum, N.N. and Bashore, T.S. Experimental studies of chaotic neuronal behaviour: cellular activity and electroencephalographic signals. In: H.G. Othmer (Ed.), Nonlinear Oscillation in Biology and Chemistry. Berlin, Heidelberg, New York, Tokyo, Springer, 1986: 175–205.
Ray, W.J. and Cole, H. EEG alpha reflects attentional demands, beta reflects emotional and cognitive processes. Science, 1985, 228: 750–752.
Roland, P.E. Cortical regulation of selective attention in man. J. of Neurophysiology, 1982, 48: 1059 -1078.
Smith, L.A. Intrinsic limits on dimension calculations. Physics Letters A, 1988, 133: 283–288.
Author information
Authors and Affiliations
Additional information
Research was supported by the Deutsche Forschungsgemeinschaft (SFB 307) and by a NATO Collaborative Research Grant to W.J. Ray and Th. Elbert. We thank two anonymous reviewers for their suggestions, particularly to conduct study 2 and to use various control computations.
Rights and permissions
About this article
Cite this article
Lutzenberger, W., Elbert, T., Birbaumer, N. et al. The scalp distribution of the fractal dimension of the EEG and its variation with mental tasks. Brain Topogr 5, 27–34 (1992). https://doi.org/10.1007/BF01129967
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01129967